Why is it creating two vertices in the same spot?
In Blender, sometimes you can create faces or edges without knowing. For example, if you tried to extrude a face, (shortcut E), but then you canceled the operation with escape, you might not notice, but a new face have been created over the one you was selecting, and its now in the same position!. This might be how the problem that you have was started.

One solution might be in the Mesh> Cleanup> Degenerate Dissolve menu found in the 3D view header while in edit mode.